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I have a problem that asks me to calculate studentized deleted residuals from the following set of residuals:

residuals

From the original dataset: enter image description here

The Hat matrix, diagonal elements hii, SSE/MSE, formula for studentized residuals, and final calculation of the residuals are below:

s

However, I cannot reproduce these results given the formula! For example, taking the square root of a negative residual in the numerator results in an imaginary number if x>0. Is there another way to calculate these residuals, or something I am I just not getting it? Thanks!

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I believe this is simply a typo. The formula should be:

$$ \frac{e_i}{\sqrt{SSE(1-h_{ii})-e_i^2}} $$

or similarly:

$$ sign(e_i)\left[ \frac{e_i^2}{SSE(1-h_{ii})-e_i^2} \right]^{1/2} $$

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  • $\begingroup$ Well.... it still doesn't appear to compute the same amounts for the studentized residuals. For example, t1 should be -.424611 using your formula $\endgroup$ – LotsofQuestions Nov 30 '15 at 20:25

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